Yesterday I started my month-long algebra unit. By the end of the unit, the kids should be able to move between graphs, tables, equations, written descriptions, and visual sequences, while also differentiating between linear and nonlinear relationships, identifying functions, and writing equations for word problems. This is a monstrously large topic, especially with below-grade-level kids and only a few weeks to get from point A to point Z. It’s also what I consider to be the most important concept of the year, and is key to being successful in high school algebra.
I’ve worked on this unit like you wouldn’t believe. It started out last year, when I did a lot of researching and help-getting (thank you, Teacher Next Door) and modifying and trying and reflecting. Some parts were hugely successful and some parts bombed, so this year I’ve given it to everyone who would look and asked for help. I’ve met with other math teachers to swap ideas and work on it together. I’ve emailed worksheets back and forth a hundred times with another teacher, each of us tweaking as we went. I’ve worked through every detail I could think of. And now it’s game time.
I make no assumptions about how it will turn out (clearly we’re not at the hard parts yet), but I’m really excited for this unit and really proud of how it looks so far. I’m working on laying a lot of conceptual understanding groundwork before we get into the actual y=mx+b/how to calculate slope/how to find y-intercept business, because I really really care that my kids get this, not just that they can do it. (Honestly, that’s not true for some other things I teach. Box and Whisker Plots, you are stupid.) And I’m pretty convinced that the structure we’ve developed is foolproof. If you pay attention and do it my way, you can’t not be good at it…there’s no room for that. The only prerequisite skills are being able to add and multiply (and yes, we’re still working on those).
We’re not at the part that’s really hard to teach yet, but these first two days have been pure joy. By this point, almost all of my kids can take a linear pattern made from blocks and write a table, predict stage 100, write a rule, graph it, and write a written description. About half could tell you the slope and y-intercept on a basic level. And they get what they’re doing and where it all comes from. One of my absolute lowest kids called me over to check his work today. Not only did he have more done than most of his classmates (I can rarely even get him to sit still long enough to do anything) but it was all correct. Then he told me it was easy because he’d seen a pattern… this is where you get slope, this is where you get y-intercept, slope is always going to go here, y-intercept is always going to go there, and then you have a rule. This is amazing because I’m approaching it backwards (they’re writing rules based on breaking down the table, not based on knowing m and b, and they’re identifying those separately from a graph) and most of my kids hadn’t made that connection yet. I didn’t expect them to see it because I’m not even guiding them toward it for another couple days, and here’s this kid who is discovering patterns on his own. He can barely do anything else I’ve taught, but he understands the origins of mx + b and he figured it out himself. I was so proud I nearly cried. Then I called his mom and made her proud too. I love days like this.